When certain characters leave a show, does it cause the show to fail?

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Several shows seem to revolve around a certain character. When the character leaves they seem to fail. A good example in my opinion was CSI. I watched every episode of CSI until Grissom left. After that point I never cared to watch it again. On Bones, after Sweets died, I found myself far less interested in the show. I still watch it but it just doesn't seem the same.